As the amount of information to be exchanged increases, the required data rates also increases. Increased data rates put considerable strains on the resources of the communication systems. One of the scarce resources is the available bandwidth. The bandwidth is always available in limited quantities. Therefore, high-speed communication in a limited bandwidth environment is an important subject for research. It is well known that under these conditions Inter-Symbol Interference (ISI) is a major cause of performance degradation.
The minimum Euclidean distance between any two symbol sequences is an important parameter to consider in order to design a technique to overcome ISI, especially when the signal to noise ratios are moderate to high level for a radio link between a transmitting device and a receiving device. Normally, as ISI increases the minimum Euclidean distance decreases.
A finite length ISI channel can be represented as a discrete time transversal filter for a given channel impulse response. An important parameter that defines the receiving device performance, in terms of Bit Error Rate (BER) versus Signal to Noise Ratio (SNR), is the minimum Euclidean distance between any two symbol sequences. It can be shown that certain channel responses give the worst minimum Euclidean distance.
Channel response is same as channel impulse response in this document. Channel impulse response is the impulse response of the channel between the transmitting device and the receiving device.
In signal processing, the impulse response, or impulse response function, of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behaviour of the system).
It is known that minimum Euclidean distance strictly decreases with ISI. Hence it is clear that when the ISI is large the deterioration of the receiving device could be very high with a limiting channel capacity of zero for certain channel responses.
On the other hand, it is possible to show the existence of cases where the distance achieves a maximum for any length of finite interference and hence those are expected to perform essentially the same as channels without ISI. Naturally then the question is whether it is possible to make those channels which perform poorly into better ones.
Several solutions for lowering ISI exist. The main solution of lowering ISI is through channel equalisation where the ISI is compensated at the receiving device. Usually the optimal equaliser employing the Viterbi algorithm can provide a satisfying equalisation performance.
The problem with Viterbi algorithm based equalising is that the complexity of the algorithm is exponentially proportional to channel memory of the length of ISI. When the ISI is severe the Viterbi algorithm based solutions can result in very complicated receiving devices or those solutions will not give good performance with receiving device with low to moderate complexity.
By introducing complex pre-processing algorithms, the channel may be improved. However, increased complexity puts more demands (and thereby also costs) in particular at the receiving device side. It would thus be desired to find a way of improving the channel between a transmitting device and a receiving device without substantially increasing receiving device complexity.